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Dr. Christopher S. Baird

Can gravity form waves?

Category: Space      Published: November 6, 2018

gravitational waves
Artistic conception of gravitational waves. Public Domain Image, source: R. Hurt/Caltech-JPL.

Yes, gravity can forms waves. Gravitational waves are ripples in spacetime that travel through the universe. If you think of gravity as a force acting at a distance, it is difficult to visualize how gravitational waves could form. However, if you use the more accurate description of gravity that was developed by Einstein in his general theory of relativity, these concepts become more logical.

General relativity describes gravity as a warping or curvature of space and time. All objects warp spacetime. When other objects travel through this warped spacetime, they end up traveling along curved paths. These curved paths look like they result from a force being exerted on the objects, when in reality they result from spacetime itself being warped. For instance, when you throw a baseball to your friend, it follows a smooth parabolic trajectory under the influence of gravity. Isaac Newton's laws would say that earth's mass is creating a gravitational force which acts on the baseball, gradually pulling the baseball down from straight-line motion. However, the more accurate description goes like this: The earth warps space and time. The baseball is actually traveling in a straight line relative to spacetime, but since spacetime itself is curved, this straight line becomes a curve when viewed by an external observer. In this way, there is not really any direct force acting on the baseball. It just looks that way because of the spacetime warpage. If all of this sounds too strange to be believed, you should know that Einstein's general relativity has been mainstream science for over a hundred years and has been verified by countless experiments.

In principle, all objects warp spacetime. However, low-mass objects such as houses and trees warp spacetime to such a small extent that it's hard to notice their effects. It takes high-mass objects such as planets, moons, or stars in order for the gravitational effects to be noticeable. The more mass an object has, the more it warps spacetime, and the stronger its gravitational effect on other objects. For instance, a black hole has such a high amount of mass in such a small volume that even light cannot escape. Inside the event horizon of a black hole, spacetime is so strongly warped that all possible paths that light can take eventually lead deeper into the black hole.

Since spacetime warpage is caused by mass, the warpage travels along with the mass. For instance, earth warps the surrounding spacetime into an inward-pinched shape (roughly speaking). As the earth travels around the sun in its year-long orbit, this pattern of spacetime curvature travels along with the earth. An observer that is stationary relative to the sun and is at a point close to earth's path would see the earth get closer and then farther away, closer and then farther away, in one-year cycles. Therefore, this observer would see earth's pinched spacetime pattern come closer and then farther away, closer and then farther away, in one-year cycles. Because the observer himself sits in spacetime and experiences it, the observer therefore sees his own local spacetime as being pinched, and then not pinched, pinched and then not pinched, in one-year cycles. The observer is therefore experiencing an oscillation of spacetime curvature that is traveling outward from the earth, i.e. a gravitational wave. This actually happens in the real world. However, in practice, gravitational waves are so incredibly weak that they have no significant effect on daily life. The oscillating spacetime warpage of a passing gravitational wave is far too weak for humans to notice or feel. Only very sensitive, expensive, modern equipment is able to detect gravitational waves. In fact, it took a hundred years after Einstein predicted the existence of gravitational waves for technology to improve enough to be able to detect them.

This idea of periodically-pinched spacetime is over-simplified. If you apply the full mathematics of general relativity, you find that an observer experiencing a passing gravitational wave does not experience a cycling pattern of spacetime pinching and no pinching. Rather, the observer experiences a cycling pattern of stretching in the sideways directions with pinching in the other sideways directions, and then pinching in the first sideways directions with stretching in the other sideways directions. For instance, suppose a gravitational wave from a distant star traveled straight down toward earth's surface right where you sit. If the gravitational wave were a thousand trillion times stronger than it can actually get in the real world, then you would see a ruler that is aligned with the east-west directions momentarily become shorter while a ruler that is aligned with the north-south directions momentarily become longer. And then a moment later, the east-west ruler would become longer while the north-south ruler would be shorter. Each ruler would continue to get periodically longer and shorter until the gravitational wave has passed. There is nothing wrong with the rulers. Spacetime itself is warping and everything in spacetime experiences the warping.

Although this effect is very weak, it actually happens. A gravitational wave detector is effectively just a very long ruler with the ability to measure the length of the ruler very accurately. For instance, each arm of a LIGO detector is 2.5 miles long and uses lasers to accurately measure lengths. Even with large, modern, expensive detectors, gravitational waves are so weak that only the largest waves can currently be detected. The current detectors cannot pick up the gravitational waves generated by planets orbiting stars or moons orbiting planets. The largest gravitational waves are generated when two black holes orbit each other rapidly immediately before falling together and merging. Large waves are also generated when two neutron stars orbit each other, or when a black hole and a neutron star orbit each other, immediately before merging. These are the only types of gravitational waves that have been detected so far.

In general, a gravitational wave is created any time a mass accelerates. Traveling along a circular path is only one type of acceleration. If an object with mass speeds up along a straight path, this is also a type of acceleration, and therefore it should create gravitational waves. Similarly, an object with mass slowing down along a straight path should also create gravitational waves. However, on the astronomical scale, an object traveling steadily along a circular orbit is far more common than an object violently slowing down or speeding up.

Another point to keep in mind is that the gravitational waves created by the earth in its yearly orbit are not only extremely weak, they also have a period of one year. This means that a gravitational wave detector on another planet would have to watch for several years in order to pick up the oscillatory shape of the gravitational waves generated by earth's orbital motion. In contrast, immediately before two black holes merge, they orbit each other so rapidly that it only takes a fraction of a second for each to complete an orbit. This is another factor that makes these types of gravitational waves easier to detect.

Topics: general relativity, gravitational waves, gravity, relativity, spacetime, wave